多维太沙基固结微分方程求解

A Solution to Terzaghi's Multidimensional Consolidation Differential Equation

本文对二维、三维太沙基固结微分方程,给出了土层顶面透水、底面透水或不透水及初始时刻的孔隙水压力为任意情况的通用求解公式,并由此获得了集中荷重及任意分布荷重时的精确解。与一维问题的计算结果相比,按二维、三维问题精确解计算的孔隙水压力消散过程明显地加快。这与工程的实际情况是一致的,因此具有重要的实用意义。

In this paper, the general solutions to the Terzaghi's two-dimensional and three-dimensional consolidation differential equations were given for cases when the surface of a soil layer is pervious, the bottom of a soil layer is pervious or non-perviougf and the initial pore water pressure is arbitrarily distributed. As a result, an accurate solution is obtained for concentrated loading and arbitrarily distributed loading . Compared with the result of one-dimensional problem, the dissipation of pore water pressure calculated by the accurate solutions to the two-dimensional and three-dimensional problems expedites obviously. This finding agrees with the engineering practice, and hence is of practical significance.